Final answer:
To determine an equation in factored form for the polynomial function with zeros 2 (order 3), 2/3, and -2, we can use the zero-product property. However, there is no equation that satisfies all the given conditions.
Step-by-step explanation:
To determine an equation in factored form for the polynomial function with zeros 2 (order 3), 2/3, and -2, we can use the zero-product property. This property states that if a polynomial function f(x) has zeros a, b, and c, then f(x) can be expressed as a product of factors: (x-a)(x-b)(x-c). So, for the given zeros, the factored form of the equation is (x-2)(x-2/3)(x+2).
To find the equation that passes through the point (-1, 135), we can use the factored form we previously found. Since the equation passes through (-1, 135), we can substitute x = -1 and y = 135 into the equation and solve for the remaining constant. After substituting the values, we get -1 = (2)(2/3)(-1+2)(-1-2). Simplifying this equation gives us -1 = (4/3)(-3)(-4), which simplifies to -1 = 16. Since this equation cannot be true, the point (-1, 135) does not lie on the graph of the given polynomial function with the specified zeros. Therefore, there is no equation that satisfies all the given conditions.